Lancashire mixes a busy competition scene around the Preston and Chorley corridor with genuine native breeding in the hills to the north and east. That gives families two quite different options: schooled, competing ponies from established yards, or hardier natives bred on rougher ground. Fell ponies in particular are well represented, and the county has a strong Pony Club presence.
It is a practical county to buy in. The motorway network makes viewings straightforward, and it is realistic to see several ponies in a day — which matters, because comparing two or three ponies in person teaches you more about what you actually want than any amount of scrolling. Ask about winter management: much of Lancashire is wet, and a pony that has coped with a Lancashire winter out is telling you something useful about its constitution.